My Arrow Crab lost his head,

Two words: Bath Salts.

Joking apart, for how long has it been eating without a head?

It could of been a week, at a quick glance I thought he was eating some kind of egg or pod, I just really notice it today, there is nothing in the tank that can do this to him, I think he had an argument with the power head, my question is more in line about how can an arrow crab live and eat with no head, and will he grow it back?

It is possible that your crab did not lose its whole head, but rather the top part which houses its eyes and other non-vital organs (a bit like the story of the "headless chicken"). I guess it is possible that it might regenerate another head since I do know that most crabs can regenerate lost limbs, but I'm not entirely sure about regenerating an entire head. What I do know is that this is pretty interesting either way.

I do know that he is as happy and pigs in the mud